It wouldn’t be fair to say that Whitney Brown has completely given up on trying to pry her offspring from their respective electronic devices.

But there are only so many times she can tell 11-year-old Cole to stop playing a “Star Wars” game on the Wii, ask 18-year-old Adison to step away from Instagram, and remind Cole’s twin, Spencer, to get off YouTube without spending her life at odds with her children.

“Sometimes you just reach a point of exhaustion,” said Brown, of Paxton. “It’s a constant struggle, and I don’t always have the energy.”

Parents say they are as concerned as ever about their children spending too much time playing video games, texting, or uploading selfies to Facebook. But trying to keep track of that time is growing ever more complicated. Not only has the number of devices soared, the social landscape has shifted, with homework assignments and textbooks moving online — making it harder to know when screen time is frivolous.

Many parents say they feel so outmatched by their electronic and juvenile opponents that, in the words of one expert, “they’re checking out of parenting in the digital domain.”

“I’ve been impressed at the number of parents who acknowledge they have no rules,” said Michael Rich,
the director of Boston Children’s Hospital’s Center on Media and Child Health, “or who say they do have rules — but then when you ask the kids, they say, ‘I don’t even know what the rules are.’ ”

Catherine Steiner-Adair
, author of “The Big Disconnect: Protecting Childhood and Family Relationships in the Digital Age,” sees a similar situation.

“Parents are giving up, and way too quickly,” said Steiner-Adair, an instructor at Harvard Medical School. “Parents say I can’t get my 8-year-old to put down the Wii or whatever game they are playing. That’s crazy. Of course they can.”

But parents say that setting and following through on rules regarding screen time is getting more difficult as household connectivity expands.

The average household has five devices, according to a 2012 survey by industry analyst Chetan Sharma, and over 6 percent of households have 15 devices or more, a number that includes smartphones, tablets, gaming consoles, e-readers, and TVs.

The increasing use of electronic communication for schoolwork is another wrinkle.

“It’s hard to decipher what they’re using it for,” said Angela Ciampa, a Dedham mother with two teen girls. “They could be looking up something related to school — or [playing] Candy Crush.”

Of course, social life has moved online, too, further complicating the situation for parents who, almost to a person, say the exact same thing: You’ve got to choose your battles.

“I don’t want to nag all the time,” said Robin Tamburrini, a Realtor from Sudbury with a 13-year-old daughter. “Sometimes I wish I never gave her that phone,” she said, “but at the same time, I want her to be social and interact, and that’s how they communicate, so sometimes I let it go.”

She paused and reflected on her no-win situation. “I don’t want to argue, so sometimes I just give up.”

Indeed, even at a time when teens’ mobile access to the Internet has increased dramatically — 37 percent have smartphones, up from 23 percent in 2011 — the number of parents who say they use parental controls or other means of blocking or filtering has decreased slightly, from 54 percent in 2011 to 50 percent in 2012, said Mary Madden, a senior researcher at the Pew Research Center’s Internet Project.

“One of the findings that is surprising to me, given parents’ reported levels of concerns about online safety,” she said in an e-mail, “is the fact that 57 percent of parents of online teens say they have never searched for their child’s name online to see what information is available about them.”

The growing body of anecdotal information about parental digital fatigue is backed up by a “digital deception” study conducted by McAfee, the Internet security company, and released in June. The study, composed of 2,474 online interviews in the United States of youths ages 10 to 23 and parents of youths ages 10 to 23, found that:

■ On average, teens estimate spending six hours a day online — significantly higher than parents, who estimate their teen spends four hours a day online.

■ While 71 percent of parents claim to have had a conversation with their child about being safe online, only 44 percent of young people agree they’ve had such a conversation.

■ Only 20 percent of parents say they know how to find out what a child is doing online, and 72 percent say they are overwhelmed by technology and just hope for the best.

■ Sixty-nine percent of young people take some measure to hide their online behavior from their parents.

Hiding usage has grown easier, since the days of a large desktop computer in a well-trafficked family room have yielded to screens so small they can be concealed in a pocket, and so common that kids who have been chased off a gaming platform scurry to a tablet, and when they’re discovered nab a parent’s phone — or their own — and head for a private spot.

In Wellesley, Andrew Snyder, the father of three, ages 10 to 17, said the number of devices makes policing them ever more difficult.

“We have enough screens so that everyone in the house can be on three screens at one time,” he said.

Like many parents, Snyder, an assistant professor at Rhode Island College, assigned himself some blame for the very screen-focused behavior he’s battling. Speaking from the perspective of a modern child, he said:

“ ‘If I’m not in an activity that you signed me up for — karate, Hebrew school, Little League, fencing, theater — I don’t know how to amuse myself.’ ”

Even when parents are fully aware of their kids’ online activities, many report being undone by the number of excuses — from their kids — about why more time online is needed. The litany will be familiar to many parents:

“I wasn’t playing, I was just watching so-and-so play.” Or: “I just need to save this game and then I’ll get off.” Or: “My game wouldn’t load. I haven’t even started playing.” “Or: We’re just texting about plans and then I’ll get off.”

And things may get worse, as new devices that teach toddlers to (safely) text and watch online videos hit the market. LeapFrog recently introduced a $150 LeapPad Ultra Learning Tablet. The “Pet Chat” app allows kids to safely “text” over a local connection with pre-defined chat phrases and emoticons with fun sounds. And VTech is out with a $100 InnoTab 3s Wi-Fi Learning App Tablet. Its “Kid Connect” app allows secure communication between a child’s tablet and a parent’s smartphone.

Meanwhile, as Brown, the Paxton mom, and her three children shopped at the Natick Mall for back-to-school supplies recently, Cole listened to his mother vent her frustration about his love of “Minecraft” and other games. He then answered the question facing his generation: Why don’t you turn off the games when asked?

He shrugged, gave an adorable smile, and explained all. “Playing is fun.”